{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:T4H6RKGQ4A5VZXH2372NFUFEQW","short_pith_number":"pith:T4H6RKGQ","canonical_record":{"source":{"id":"1107.0817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-05T08:57:38Z","cross_cats_sorted":[],"title_canon_sha256":"e4231f615a28d4d8ba29f11cfcc30d2e080f78fc3a7ff11f74ed566794a5127e","abstract_canon_sha256":"5f98992b91f65a3edd238b6ef118cb599f21fb777f45de5e853c1cecb499c861"},"schema_version":"1.0"},"canonical_sha256":"9f0fe8a8d0e03b5cdcfadff4d2d0a485ac18e6c1039113182964a06a372a8752","source":{"kind":"arxiv","id":"1107.0817","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0817","created_at":"2026-05-18T04:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0817v1","created_at":"2026-05-18T04:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0817","created_at":"2026-05-18T04:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"T4H6RKGQ4A5V","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T4H6RKGQ4A5VZXH2","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T4H6RKGQ","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:T4H6RKGQ4A5VZXH2372NFUFEQW","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-05T08:57:38Z","cross_cats_sorted":[],"title_canon_sha256":"e4231f615a28d4d8ba29f11cfcc30d2e080f78fc3a7ff11f74ed566794a5127e","abstract_canon_sha256":"5f98992b91f65a3edd238b6ef118cb599f21fb777f45de5e853c1cecb499c861"},"schema_version":"1.0"},"canonical_sha256":"9f0fe8a8d0e03b5cdcfadff4d2d0a485ac18e6c1039113182964a06a372a8752","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:52.636327Z","signature_b64":"1ti0jLPdLJHUN+TPqV0r68xHzY58/3dvgs57KoZ8YS7b+X6KYp9lmQCaWLhBY6SiK4j0to91I3e6FBiUy485AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f0fe8a8d0e03b5cdcfadff4d2d0a485ac18e6c1039113182964a06a372a8752","last_reissued_at":"2026-05-18T04:18:52.635836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:52.635836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0817","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"afY8d0afPCI2l3PhRw+TS+5KchDwFmL87rICmA/PeqrumTZ+1mvuyaMJYpQEc9e5JOKzDD8oeUQIC+GBLANLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:38:19.278178Z"},"content_sha256":"46fd973327ce8f99c9ae99d85fdbf2c92a4d8b90c99dd9ec440d8c422fd2f62b","schema_version":"1.0","event_id":"sha256:46fd973327ce8f99c9ae99d85fdbf2c92a4d8b90c99dd9ec440d8c422fd2f62b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:T4H6RKGQ4A5VZXH2372NFUFEQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Des points fixes communs pour des diff\\'eomorphismes de S^2 qui commutent et pr\\'eservent une mesure de probabilit\\'e","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Francois Beguin, Patrice Le Calvez, Saponga Firmo, Tomasz Miernowski","submitted_at":"2011-07-05T08:57:38Z","abstract_excerpt":"We prove the existence of common fixed points for commuting homeomorphisms of the plane R^2 or the sphere S^2, which preserve a probability measure. For example: some commuting C^1-diffeomorphisms of S^2, which are sufficiently close to the identity and preserve a probability measure whose support is not a single point, have at least two common fixed points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0817","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h2uZBX5ElyyB19nKzxNponU2ySW+7i6VjyHzNZXPEGlDmehsIvWS0+D9XC4Egs2eLuASoMmFZTVnfvHoRNZdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:38:19.278542Z"},"content_sha256":"85e2e2822558826cfaf18d308a304939784358de1a232f9271dc04d10d894d27","schema_version":"1.0","event_id":"sha256:85e2e2822558826cfaf18d308a304939784358de1a232f9271dc04d10d894d27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4H6RKGQ4A5VZXH2372NFUFEQW/bundle.json","state_url":"https://pith.science/pith/T4H6RKGQ4A5VZXH2372NFUFEQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4H6RKGQ4A5VZXH2372NFUFEQW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T14:38:19Z","links":{"resolver":"https://pith.science/pith/T4H6RKGQ4A5VZXH2372NFUFEQW","bundle":"https://pith.science/pith/T4H6RKGQ4A5VZXH2372NFUFEQW/bundle.json","state":"https://pith.science/pith/T4H6RKGQ4A5VZXH2372NFUFEQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4H6RKGQ4A5VZXH2372NFUFEQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:T4H6RKGQ4A5VZXH2372NFUFEQW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5f98992b91f65a3edd238b6ef118cb599f21fb777f45de5e853c1cecb499c861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-05T08:57:38Z","title_canon_sha256":"e4231f615a28d4d8ba29f11cfcc30d2e080f78fc3a7ff11f74ed566794a5127e"},"schema_version":"1.0","source":{"id":"1107.0817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0817","created_at":"2026-05-18T04:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0817v1","created_at":"2026-05-18T04:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0817","created_at":"2026-05-18T04:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"T4H6RKGQ4A5V","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T4H6RKGQ4A5VZXH2","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T4H6RKGQ","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:85e2e2822558826cfaf18d308a304939784358de1a232f9271dc04d10d894d27","target":"graph","created_at":"2026-05-18T04:18:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove the existence of common fixed points for commuting homeomorphisms of the plane R^2 or the sphere S^2, which preserve a probability measure. For example: some commuting C^1-diffeomorphisms of S^2, which are sufficiently close to the identity and preserve a probability measure whose support is not a single point, have at least two common fixed points.","authors_text":"Francois Beguin, Patrice Le Calvez, Saponga Firmo, Tomasz Miernowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-05T08:57:38Z","title":"Des points fixes communs pour des diff\\'eomorphismes de S^2 qui commutent et pr\\'eservent une mesure de probabilit\\'e"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0817","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:46fd973327ce8f99c9ae99d85fdbf2c92a4d8b90c99dd9ec440d8c422fd2f62b","target":"record","created_at":"2026-05-18T04:18:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5f98992b91f65a3edd238b6ef118cb599f21fb777f45de5e853c1cecb499c861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-05T08:57:38Z","title_canon_sha256":"e4231f615a28d4d8ba29f11cfcc30d2e080f78fc3a7ff11f74ed566794a5127e"},"schema_version":"1.0","source":{"id":"1107.0817","kind":"arxiv","version":1}},"canonical_sha256":"9f0fe8a8d0e03b5cdcfadff4d2d0a485ac18e6c1039113182964a06a372a8752","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f0fe8a8d0e03b5cdcfadff4d2d0a485ac18e6c1039113182964a06a372a8752","first_computed_at":"2026-05-18T04:18:52.635836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:52.635836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ti0jLPdLJHUN+TPqV0r68xHzY58/3dvgs57KoZ8YS7b+X6KYp9lmQCaWLhBY6SiK4j0to91I3e6FBiUy485AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:52.636327Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46fd973327ce8f99c9ae99d85fdbf2c92a4d8b90c99dd9ec440d8c422fd2f62b","sha256:85e2e2822558826cfaf18d308a304939784358de1a232f9271dc04d10d894d27"],"state_sha256":"1db0f5316837ea0cd66ef4d8ded5666340144eb896efc20ab61ea2e4445ccdc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XpPv1zLNnxPUXZVIrk+0k8KSfRE6C6CfMkvgtjgxzOgbfNxei6Cs9n3gq4IHtEuGlFTaQWMLXSUrNtEnUFCyAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:38:19.280458Z","bundle_sha256":"5e659852c03a8246ffeecb93620c7c165d47eac64a9619151f3752ea69e3a4a5"}}